1. Field of the Invention
This invention relates to characterizing an optical wavefront produced by an optical component or external source and more particularly to measuring the local tilt present in the wavefront.
2. Description of the Related Art
In many optical systems it is important to characterize the optical wavefront produced by a particular optical component or external source. The optical wavefront is defined as a continuous surface with constant optical path length from a source. In many cases, it is desired to measure the deviations in the actual wavefront from an ideal planar wavefront (if the source is at infinity) or alternatively from an expected wavefront of arbitrary shape.
A continuous measurement of the wavefront is typically performed with an interferometer. Interferometric techniques, typically involve expensive equipment and software programs that analyze interference fringe patterns, producing a measure of the wavefront deviation from a reference standard. Modern day practices use a charge-coupled device (CCD) to digitize and analyze the data; the reconstruction is not continuous, but the initial interference pattern is. An alternative approach is to discretely sample the wavefront directly. In this case, a sub-region of the continuous wavefront is sampled. If the sample is small enough (spatial sampling resolution high enough) for the given wavefront, the sampled sub-region will consist of a linear tilt at a particular angle. Stitching the samples back together produces a piece-wise linear fit of the slope present in the initial continuous wavefront. This piece wise linear fit can then be integrated to arrive at an estimate of the measured wavefront. One example of a device that performs this function is the Shack-Hartmann Wavefront Sensor.
Relatively recently, the desire to modulate an optical component such that the component can cancel out external wavefront aberrations (e.g. atmospheric, human tissue, etc.) has driven a requirement for systems that can measure the desired wavefront robustly and at the speed necessary for active control. Ideally, the measurement sensitivity should be comparable to standard interferometric techniques, with an additional requirement that the instantaneous dynamic range of the wavefront measurement must be larger than is available via interferometric techniques. The dynamic range of the system is defined as the maximum measurable tilt angle, while the measurement sensitivity is defined by the minimum measurable tilt angle. Finally the desired system needs to be relatively inexpensive and simple to implement. To date, almost all successful attempts to meet these requirements have been with a category of instruments referred to as wavefront sensors, the most prevalent being the Shack-Hartmann Wavefront Sensor.
The Shack-Hartmann Wavefront Sensor consists of an array of miniature lenslets used to sample the wavefront discretely. Each lenslet focuses a portion of the wavefront onto a sub-array within a detector (typically a CCD or CMOS device). The local tilt present in the wavefront manifests itself as motion in the focal plane, making the centroid of the image a measurement of the local slope of the wavefront for each lenslet. While this system degrades the spatial sampling resolution of the wavefront, the larger dynamic range makes it a simple and versatile system for conditions where an interferometer is not desired. Although the dynamic range is larger than the traditional interferometer, it is still limited by the diameter of the individual lenslets. Sophisticated algorithms have been developed to marginally improve dynamic range for these systems, but in general if greater dynamic range is desired, it must be accompanied by either an increase in the lenslet diameter or a decrease in the focal length. The former reduces the spatial sampling resolution while the later degrades the measurement sensitivity; both of these trades lead to degradation in measurement accuracy. Fabrication of the lenslet arrays, while dramatically improved in recent years is still a cost barrier for these systems.
Another more recent desire is to measure the tilt angle of MEMs based micro-mirror devices. Given the large required dynamic range and spatial sampling requirements typical of the MEMs systems, the family of Shack-Hartmann wavefront sensors is not a viable approach to this problem. In U.S. Pat. No. 6,339,219 Nikon proposes using a “pinhole” aperture, created with a Liquid Crystal Display (LCD), in the focal plane of a single lens to measure the tilt of individual pixels on an IR cantilevered array. The pinhole is used as a limiting aperture in the Fourier plane to impart an amplitude modulation related to the tilt angle. Because the pinhole diameter must be on the order of the central spot size in the diffraction pattern to modulate the transmitted amplitude, the dynamic range is still small, perhaps a degree to a degree and a half. In addition, with any binary edge filter, the system transfer function can only be modestly changed by the geometry of the limiting aperture. To achieve a larger useful dynamic range, Nikon proposes moving the pinhole aperture dynamically to cover the desired dynamic range of tilt angles, effectively translating the bandpass of the measurement system temporally. This is a severe limitation of the system, requiring time multiplexing of the input signal and complicated algorithms to stitch the images together.
Because of the limitations in both systems described above, additional methods of wavefront sensing have been pursued for a variety of applications. Another closely related technique typically referred to as wavefront curvature sensing, uses the same lenslet array, but measures changes in peak focal spot intensity, related to the local degree of curvature in the wavefront (i.e. the local wavefront curvature manifests itself as a defocus that spreads the energy across more pixels, reducing the measured peak amplitude). While this method allows a decrease in lenslet focal length to increase the dynamic range of the system with reduced impact to measurement sensitivity, the spatial sampling resolution of the wavefront is still limited by the required lenslet diameter. In addition, this system measures a second order effect and would not be sensitive to a simple first order wavefront tilt.